Effects of External Ions on the Dynamics of Proton Transfer Across a Hydrogen Bond

The influence of external ions upon the dynamics of proton transfer between the H2O subunits in (H2O-H-OH2)+ is studied by quantum-mechanical techniques. Each proton-transfer potential, computed via ab initio molecular orbital methods, is fit to a fourth-order polynomial of the proton position from which the vibrational levels and eigenfunctions are extracted. In the case of the unperturbed H bond or when the ion is in a symmetric position, the proton tunneling frequencies may be evaluated in terms of the splitting of the vibrational levels. These rates compare quite favorably with dynamic data calculated by using the quasi-classical WKB approximation. The tunneling frequencies are in the picosecond time scale and are little affected by ions placed along the O- -O bisector plane. Coupling of two simultaneous proton transfers leads to a substantial deepening of the potential wells which can then accommodate more than one pair of vibrational states. The tunneling rate in the lowest pair is several orders of magnitude slower than in the case of a single transfer; although faster frequencies are associated with the higher levels, their low populations mitigate against large contributions to the overall transfer rate. Displacements of the ions from a central location produce large asymmetries in the potential which in turn have the effect of localizing the proton in one well or the other in each vibrational state. The transfer rates in these asymmetric potentials are much slower than in the symmetric case due to (a) lower intrinsic tunneling frequencies and (b) small populations in the appropriate states